Problem: Solve for $x$ and $y$ using elimination. ${4x+6y = 60}$ ${5x-3y = -9}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${4x+6y = 60}$ $10x-6y = -18$ Add the top and bottom equations together. $14x = 42$ $\dfrac{14x}{{14}} = \dfrac{42}{{14}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {4x+6y = 60}\thinspace$ to find $y$ ${4}{(3)}{ + 6y = 60}$ $12+6y = 60$ $12{-12} + 6y = 60{-12}$ $6y = 48$ $\dfrac{6y}{{6}} = \dfrac{48}{{6}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {5x-3y = -9}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ - 3y = -9}$ ${y = 8}$